Covering-based soft fuzzy rough theory and its application to multiple criteria decision making
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(2019) 38:149
Covering-based soft fuzzy rough theory and its application to multiple criteria decision making Jianming Zhan1
· Bingzhen Sun2
Received: 27 March 2019 / Revised: 13 June 2019 / Accepted: 24 September 2019 © SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2019
Abstract Covering-based rough set model is a vital topic as a generalization of rough sets which is a tool for AI and data mining. For the purpose, we establish two classes of hybrid uncertain systems: soft rough fuzzy-covering models and soft fuzzy rough covering models by means of (fuzzy) soft neighborhoods. By means of fuzzy soft measure degrees, we deduce αsoft rough fuzzy coverings, D-soft rough fuzzy coverings, α-soft fuzzy rough coverings, and D-soft fuzzy rough coverings by these two hybrid uncertain systems, respectively. The relationships among the proposed covering-based rough set models are given. Based on the theoretical discussion for the combination of covering fuzzy rough sets and soft sets, we set forth a new method to multiple criteria decision-making problem. By comparative analysis, we obtain that the optimal results are the same between the aggregation operator method and our proposed method, which means that our method is reasonable and effective. Keywords (Fuzzy) rough covering · (Fuzzy) soft neighborhood · (Fuzzy) soft measure degree · Soft rough fuzzy covering · Soft fuzzy rough covering · Multiple criteria decision making Mathematics Subject Classification 68T30 · 68T10 · 90B50
1 Introduction As far as known that Pawlak (1982) established firstly rough set theory (briefly, RST), which is a useful method to cope with some uncertain or fuzzy information. We know that RST presents a systematic way for classification of the object via an indiscernibility relation. Until
Communicated by Marcos Eduardo Valle.
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Jianming Zhan [email protected] Bingzhen Sun [email protected]
1
Department of Mathematics, Hubei Minzu University, Enshi 445000, China
2
School of Economics and Management, Xidian University, Xi’an 710071, China
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now, this novel theory has been applied to many research fields, for example, see Pawlak (1998). Due to the reason that Pawklak’s model is established in an equivalence relation (briefly, ER), in real life, it is far too difficult to produce this equivalence relation among the elements of the given universe set. Observe that this original classification in particular imposes transitivity of the indiscernibility relation. However, in the early development of decision theory, the inconveniences of that assumption are so obvious that they are the germ of interesting models of choice behavior. To solve this type of shortcomings, many researchers established many generalized rough set models (see Liu and Sai 2009; Qin and Pei 2005; Sun et al. 2017a, c; Wu and Zhang 2004; Yao 1998; Yao and Deng 2014; Zhang et al. 2016). It is well known that covering-rough set model (briefly, CRS-model) is a vital research topic of generalized RST. CR
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